expected radiation in flash with 3rd harmonic module file3d and 1d simulations with self fields....
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Expected Radiation in FLASH with 3rd Harmonic Module
Igor Zagorodnov11.05.2009
BD meeting, DESY
ACC39
Present layout + ACC39 is considered in the talk.Energy 1 GeV.Radiation wavelength ~ 6.5 nm.Bunch charges 1nC, 0.5 nC, 0.25 nC.
Layout and main parameters
1
56
566
5666
127MeV
r = -0.1808[m]
t 0.295198
u -0.437737
E =
==
2
56
566
5666
470MeV
r = -0.048669[m]
t 0.0733141
u -0.0982712
E =
==
3
56
566
5666
1 eV
r = 5.585e-4[m]
t 0.0588
u -0.6417
E G=
==
ACC39
3D simulation setup
ASTRA (m=0 solver, on axis bunch)
CSRtrack (1D model)
W3 2W13W1W1
TM
Linear Transformation (slice centers)
W1-TESLA cryomodule wake
W3- ACC39 wake
TM- transverse matching to thedesign optics
M. Krasilnikov - Input Desk for ASTRA gun simulations for 1nC, 0.5 nC, 0.25nCN. Golubeva – MAD optics (V2, V2+) for 1 GeV
1D (longitudinal phase space) simulation setup
accelerator
compressor
W1 -TESLA cryomodule wakeW3 - ACC39 wakeLS - space charge wakeWin, Wout - wakes to simulate CS and edge radiation in BCs
ACC39
2W1LSWin
W1 W3LSWin
Wout Wout 3W1LSWin
Wout LS
1 1 0 0 0( ) ( ) cos( )E s E s V ks ϕ= + +
1 1 0 0 1( ) ( ( ))E s E s s=
1 0s s=
( )1 2 31 0 0 56 0 566 0 5666 0( )s s s r t uδ δ δ= − + +
3D and 1D simulations with self fields.
space charge +cavity wakes + self fields in BCs
1D model was checked through 3D.Working points are found by optimization in 1D and then checked by 3D.Finally, 1D model is used to estimate the RF tolerances.
3D model 1D model
3D results to fit the 1D model
1D scan to find the working point
1D results to use in the 3D model
Accuracy check of the results for 1nC presented in January
-1 -0.5 0 0.5 1 1.5
x 10-4
0
500
1000
1500
2000
2500
Parallel ASTRA vs. serial one
serial
parallel
Have I started exactly with the same distribution from the cathode?
[m]s [m]s
[MeV]E[A]I
-1 -0.5 0 0.5 1 1.5
x 10-4
0
500
1000
1500
2000
2500
-1 -0.5 0 0.5 1 1.5
x 10-4
0
500
1000
1500
2000
25001000k particles
Mesh 25*50
Mesh 50*100
Mesh 24*64
1000k200k
Accuracy check of the results for 1nC presented in January
Different number of particles and mesh lines in ASTRA
[m]s
[A]I
[m]s
[A]I
-2 -1 0 1 2-200
-150
-100
-50
0
50
100
150
200
Numerical (ECHO)
Analytical
-4 -2 0 2 4-200
-150
-100
-50
0
50
100
150
200
bunch
Accuracy check of the results for 1nC presented in January
Check of the wakefield model from the gun up to BC2
/s σ
||
kV
nCW
||
kV
nCW
Numerical(ECHO)
Analytical
bunch
/s σ
0 100 200 3001
2
3
4
5
6
7
8x 10
-6
Phase shift between BCs (Q=1nC, optics V2).
prxε
[ ]m×rad
0 50 100 150 200 250 300 3500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-6
[ ]degψ∆
[ ]m×rad
[ ]degψ∆
Maximal slice emittance in [−σ,σ]Projected emittance
pryε
xσε
yσε
[ , ]max ( )sl
ssσ
σ σε ε
∈ −=[ ]60 deg ?ψ∆ = − −
10 20 30 40 50 60 700
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
10 15 20 25
5
10
15
20
V2
V2+
V2m
V2+
V2
V2m
-60o
-50 0 500
1
2
3
4
5
-50 0 500
1
2
3
4
5
V2+V2
Phase shift between BCs (Q=0.5nC).
[m]z[m]z
[m]xβ[rad]µ
[µm]s[µm]s
[mm×mrad] [mm×mrad]
xε
yε
xε
yε
Work points(Track1D)
6.932
18.771
25.198
ϕ2,
[deg]
530.937
531.261
531.845
V3,
[MV]
0379.867194.96315.99614.848142.3721
16.9413
16.993
V39,
[MV]
183.034
193.356
ϕ39,
[deg]
0345.8111.098141.6110.25
0362.72214.521143.1930.5
ϕ3,
[deg]
V2,
[MV]
ϕ1,
[deg]
V1,
[MV]
Charge,
nC
0 0.5 1141
142
143
144
145
0 0.5 115.8
16
16.2
16.4
16.6
16.8
17
17.2
0 0.5 1340
350
360
370
380
390
0 0.5 111
12
13
14
15
0 0.5 1182
184
186
188
190
192
194
196
0 0.5 15
10
15
20
25
30
0 00
0 0
2 ( ) ( ) 3 (0) max ( )min 0.25 , 1809s
s
I I I I I s II A
I
σ σεε
− − + − + − + =
1V39V 2V
1ϕ 39ϕ2ϕ
[MV]
[deg]
[nC]Q
[nC]Q
Tolerances (Track1D)
-0.2 -0.1 0 0.1 0.20
0.5
1
1.5
2
2.5
3
-0.2 -0.1 0 0.1 0.20
0.5
1
1.5
2
2.5
3
-0.2 -0.1 0 0.1 0.20
0.5
1
1.5
2
2.5
3
-1 -0.5 0 0.5 10
0.5
1
1.5
2
2.5
-1 -0.5 0 0.5 10
0.5
1
1.5
2
2.5
-1 -0.5 0 0.5 10
0.5
1
1.5
2
2.5
[MV]
1V 39V2V
1ϕ39ϕ 2ϕ
[deg]
0
C
C
0
C
C
1 nC
0.25 nC
0.5 nC
1 nC
0.25 nC0.5 nC
0.25 nC
0.5 nC
1 nC
Tolerances
0.25
0.5
1
0.25
0.5
1
0.25
0.5
1
Charge, nC
1.560.02
0.110.010.140.14ACC39
0.620.05ACC1
0.100.06
0.140.03
0.58
0.44
0.56
Phase, degree
2.2
2.6
4.6
ACC2
V, MV
Tolerances (10 % change of compression)
Q=1nC (S2E)
-100 -50 0 50 1000
500
1000
1500
2000
2500
-100 -50 0 50 1000
0.5
1
1.5
2
2.5
-100 -50 0 50 100-1
-0.5
0
0.5
1
1.5
2
[µm]s
[mm×mrad]xε
yε
[m]s [m]s
[MeV]E[A]I
[m]s
x
x
σ
y
y
σ
1D
3D
1D3D
-100 -50 0 50 100997
998
999
1000
1001
1002
1003
1004
Q=0.5nC (S2E)
-50 0 500
500
1000
1500
2000
2500
3000
-50 0 500
0.5
1
1.5
2
2.5
-50 0 50-1.5
-1
-0.5
0
0.5
1
1.5
[µm]s
[mm×mrad]xε
yε
[m]s [m]s
[MeV]E[A]I
[m]s
x
x
σy
y
σ
1D
3D1D
3D
-50 0 50997
998
999
1000
1001
1002
1003
1004
Q=0.25nC (S2E)
-20 0 20 400
500
1000
1500
2000
2500
-20 0 20 400
0.5
1
1.5
2
2.5
-20 0 20 40-2
-1
0
1
2
y
y
σ
[µm]s
[mm×mrad]xε
yε
[m]s [m]s
[MeV]E[A]I
[m]s
x
x
σ
1D
3D
1D3D
-20 -10 0 10 20 30 40997
998
999
1000
1001
1002
1003
1004
-100 -50 0 50 100997
998
999
1000
1001
1002
1003
1004
-50 0 50997
998
999
1000
1001
1002
1003
1004
-20 -10 0 10 20 30 40997
998
999
1000
1001
1002
1003
10041 nC 0.5 nC 0.25 nC
Density function ( , )s Eρ
[µm]s
[MeV]E
-1 -0.5 0 0.5 10
0.5
1
1.5
2
2.5
-100 -50 0 50 100 1500
500
1000
1500
2000
2500
192649σz, mkm
1078574σx, mkm
4979154FWHM, mkm
617565σy, mkm
0.250.51Q,nC
' 'x y x y x yx y x y Iγ γ ε ε β β α α∆Slice parameters extracted from S2E simulations
-1 -0.5 0 0.5 1-3
-2
-1
0
1
z
z z
σ−
z
z z
σ−
[mm×mrad]xε
0x
x
σ0 74µmxσ =
Slice parameters[A]I
[mm]s
1 nC
0.5 nC
0.25 nC
1 nC
0.25 nC
1 nC
0.5 nC
0.25 nC
FEL code ALICE• 1D/2D/3D • 3D azimuthal field solver (Neumann)• Leap-Frog integrator• Perfectly Matched Layer• transverse motion• simplified model• parallel (MPI)• tested on examples from the book of E.L. Saldin at al “The Physics …“, and by comparison with code Genesis 2.0 of S. Reiche
Radiation energy statistics (700 runs)
0 5 10 15 20 2510
-3
10-2
10-1
100
101
102
103
10 15 20 25
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 250
5
10
15
20
25
10-2
100
102
0
5
10
15
20
25
[µJ]E
[m]z [m]z
[m]z
[µJ]E
[%]Eσ [%]Eσ
[µJ]E
1 nC
0.5 nC
0.25 nC
1 nC
0.5 nC
0.25 nC
1 nC
0.5 nC
0.25 nC
Radiation energy statistics
0.5 1 1.50
2
4
6
8
0.5 1 1.50
0.5
1
1.5
2
0.5 1 1.50
1
2
3
4
5
z=10mσ=23%
z=18mσ=8.7%
z=26mσ=4.2%
0.5 1 1.50
1
2
3
4
0.5 1 1.50
1
2
3
4
5
6
7
p(E
)
0.5 1 1.50
2
4
6
8
10
12
14
z=10mσ=11%
z=18mσ=5.1%
z=26mσ=2.8%
0.5 1 1.50
0.5
1
1.5
2
2.5
0.5 1 1.50
1
2
3
4
5
6
0.5 1 1.50
2
4
6
8
10
z=10mσ=17%
z=18mσ=6.8%
z=26mσ=3.7%
E
E
( )p E 1 nC 0.5 nC 0.25 nC
Gamma distr.
Temporal structure
-50 0 50 1000
0.005
0.01
0.015
0.02
0.025
0.03
-50 0 50 1000
0.5
1
1.5
2
2.5
-50 0 50 1000
0.5
1
1.5
2
2.5
3
3.5
4
-100 0 1000
0.005
0.01
0.015
0.02
0.025
0.03
-100 0 1000
0.5
1
1.5
2
2.5
3
-100 0 1000
1
2
3
4
5
-200 -100 0 100 2000
1
2
3
4
5
-200 -100 0 100 2000
0.5
1
1.5
2
2.5
3
-200 -100 0 100 2000
0.002
0.004
0.006
0.008
0.01z=10m
z=18m
z=26m
z=10m
z=18m
z=26m
z=10m
z=18mσ=6.8%
z=26m
( )[GW]P s
[µm]s
1 nC 0.5 nC 0.25 nC
Temporal structure
5 10 15 20 250
50
100
150
200
250fs
FWHM
5 10 15 20 250
10
20
30
40
50µm
zσ
[m]z [m]z
1 nC
0.5 nC
0.25 nC
1 nC
0.5 nC
0.25 nC
0 100 200 300 400 5000
0.2
0.4
0.6
0.8
1
0 50 100 150 2000
0.2
0.4
0.6
0.8
1
0 100 200 3000
0.2
0.4
0.6
0.8
1
Temporal structure. Degree of contrast.
1 nC 0.5 nC 0.25 nC
10.5
0.5
( ) ( ) ( )C P t dt P t dtτ
τ
τ−∞
− −∞
=
∫ ∫
[fs]τ [fs]τ [fs]τ
( )C τ ( )C τ( )C τ
10m
26m18m
10m
26m
18m
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
-1.5 -1 -0.5 0 0.50
0.5
1
1.5
z=10mFWHM=0.49%
z=18mFWHM=0.38%
z=26mFWHM=0.41%
z=10mFWHM=0.54%
z=18mFWHM=0.43%
z=26mFWHM=0.46%
z=10mFWHM=0.52%
z=18mFWHM=0.38%
z=26mFWHM=0.41%
ωω
∆
( )[a.u.]P ωSpectrum
1 nC 0.5 nC 0.25 nC
First order correlation
2 1
fs
t t−
1[fs]t
1 1 2 1( , )g t t t−1 nCQ = 0.5 nCQ = 0.25 nCQ =
10 mz =
18 mz =
26 mz =
*1 2
1 1 21 2
( ) ( )( , )
( ) ( )E E
E t E tg t t
t tσ σ=ɶ ɶ
Coherence time
-200 -100 0 100 2002
3
4
5
6
7
8
-50 0 50 1002
4
6
8
-100 -50 0 50 100 1502
3
4
5
6
7
8
1[fs]t
1 nCQ =
0.5 nCQ =
0.25 nCQ =
10 mz =
18 mz =26 mz =
2
1( ) ( , ') 'c t g t t dtτ = ∫
1[fs]t1[fs]t
[fs]cτ
[fs]cτ
[fs]cτ
Summary
50-140100-200200-300Radiation pulse duration at
80% of contrast, fs
0.4-0.60.4-0.5Spectrum width, %
4-5Coherence time, fs
10001000Beam energy, MeV
without*with harmonic module
0.5-10.250.51Bunch charge, nC
35-150
400
0.7-2
2
25-100
200
0.6-2
1.7
2-43Averaged peak power, GW
22-3220Saturation length, m
50-150700Energy in the rad. pulse, mkJ
15-50100-250Radiation pulse duration
FWHM, fs
1.3-2.22Peak current, kA
1.5-3.51.2-2Slice emmitance,mm-mrad
66.5Wavelength, nm
*) E.L.Saldin at al, Expected properties of the radiation from VUV-FEL at DESY,TESLA FEL 2004-06, 2004.
Summary
ASTRA – tracking in stright sections with SCCSRtrack – tracking through dipolesMAD 8 – optics matchingGlueTrackM – master script for 3D S2ETrack1D – semi-analytical tracking of long. phase spaceECHO – wake fieldsALICE – FEL process
Acknowledgements to
M. Dohlus, M. Krasilnikov, T. Limberg, W. Decking,N. Golubeva, E. Schneidmiller
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